Question

In ∆ABC AB=20,BC=21 and AC=29. Find the radius of the circle touching all the sides if ∆ABC.

Answer 1

Answer:

6 cm

Step-by-step explanation:

Answer 2

Radius would be 6 unit.

Step-by-step explanation:

In triangle ABC,

AB=20,BC=21 and AC=29,

Semi perimeter of the triangle,

$s=\frac{AB+BC+AC}{2}=\frac{20+21+29}{2}=\frac{70}{2}=35$

By Heron's formula,

$A=\sqrt{s(s-AB)(s-BC)(s-AC)}$

$=\sqrt{35(35-20)(35-21)(35-29)}$

$=\sqrt{35(15)(14)(6)}$

$=\sqrt{44100}$

$=210$

Thus, inradius of the circle ( or radius of the circle touching all the sides ) is,

$r=\frac{A}{s}=\frac{210}{35}=6\text{ unit}$

#Learn more:

Find the inradius of the triangle whose sides are 3,5,6.

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